Characteristic cohomology and observables in higher spin gravity
Alexey Sharapov, Evgeny Skvortsov
Abstract
A bstract We give a complete classification of dynamical invariants in 3 d and 4 d Higher Spin Gravity models, with some comments on arbitrary d . These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p -form currents with various p . The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.